Anybody who has been involved in indie book marketing for more than a month or two is probably well aware of the tactic of using free books to build exposure and, hopefully, a base of loyal readers. There are various ways to do this, and the value of it also varies—but the fact that giving away free copies is considered a benefit of Amazon's KDP Select underscores the value of the tactic.
There are other mechanisms, apart from KDP Select, to give away free copies. These include setting up books to be "permafree" on e-book platforms where that configuration is easy (e.g., Kobo) to coupon systems and "pay what you want, even if that means zero" options. Another option is for writers to simply post free copies on their Web sites, with the files either hosted directly on their Web server or linked to a cloud storage system like Dropbox.
Those are all common and accepted ways to distribute individual copies from the author to the reader, either directly or via a third-party system. However, they don't provide a way for readers to pass along copies to other readers. It could be done, but possibly not easily and possibly not legally. You can expand the reach of your free book, and further build your audience, by using "piracy"—which I put in quotes because it's not real piracy*, but it uses tools that are used by those who violate copyright laws.
Encouraging people to pass along free copies of a creative work is nothing new. The Grateful Dead are well known for their policy of allowing fans to freely record their concerts, as long as they didn't sell the tapes. As indie writers, we can do something similar.
The first step is to grant a license to the work that allows such copying; the Creative Commons Attribution-NonCommercial-NoDerivatives license is one that would emulate the Grateful Dead's "copy, but don't sell" approach, but there are other licenses you could choose. Add a reference to the license on the copyright page, so that readers know they are free to give copies to their friends.
The next step is to make the book easily downloaded. One way is to post the book files on your Web site in a visible location. Another way is to use one of the tools that is unfortunately commonly used for copyright violation: BitTorrent. This might seem daunting to those unfamiliar with BitTorrent, but by enabling this method of distributing free copies of your book, you're expanding your reach far beyond the people who would go directly to your site.
For example, I currently have my science fiction novelette Wolf Block set up for free downloads via BitTorrent, and for this I simply posted the MOBI and EPUB files to Amazon S3 (a cloud storage service that supports, among many other things, BitTorrent "seeding"). If you have a BitTorrent client set up, feel free to give this a try and grab either the MOBI or EPUB of Wolf Block.
Once your book is available via BitTorrent, the next step is to add it to the various torrent sites. This is a step I have not completed yet, because until very recently I wasn't confident in the Amazon S3 seeding. It seems to work flawlessly, though, so finding torrent sites where I can add it is on my to-do list.
Naturally, your book files should not have any DRM enabled. This isn't a step, per se, but avoiding the step of enabling DRM will make sure the other steps aren't pointless!
If you distribute books for free, I invite you to post links to them in the comments!
* Making an illegal copy of something is nothing like the brutal violence of real pirates. I think the term "piracy" for "copyright violation" is ridiculous, and it actually supports the egos of the violators themselves, who want to be associated with the swashbuckling image of the pirates of old. I prefer the term "bootleg" which has no such connotations.